ANALYTICAL MECHANICS
re vp is the component of the linear velocity in a direction >endicular to the axial plane.
ILLUSTRATIVE EXAMPLE.
particle describes a circle of radius a with a constant speed v. igular velocity relative to an through a point on the cir-erence and perpendicular to >lane of the circle. it P (Fig. 55) be the position e particle and 0 the point at bi the axis of reference inter-the circle. Move the par-from P to Pf and denote the r and angular displacements ? and dB respectively. Then
ingle subtended by PP' at FIG. 55.
one-half that subtended at (7. Hence
Find
2 a ' cW
2 a dt
— JL ~2o'
the angular velocity about 0 is independent of the position of the :le and equals one-half the angular velocity about the center.
PROBLEMS.
The radius of the earth is 4000 miles and that of its orbit 93 million Compare the angular velocities of a point on the equator with st to the sun at midday and midnight.
In what latitude is a bullet, which is projected east with a velocity JO feet per second, at rest relatively to the earth's axis; the radius taken as 4000 miles?